Constants on a Uniform Berry-Esseen Bound on Some Borel Sets in ℜ k via Stein's Method

Author： Thongtha D.   Neammanee K.  

Publisher： Taylor & Francis Ltd

ISSN： 0361-0926

Source： Communications in Statistics: Theory and Methods, Vol.42, Iss.23, 2013-12, pp. : 4247-4258

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Abstract

For each n, k ∈ , let Y i = (Y i1, Y i2,…, Y ik ), 1 ≤ i ≤ n be independent random vectors in ℜ k with finite third moments and Y ij are independent for all j = 1, 2,…, k. In this article, we use the Stein's technique to find constants in uniform bounds for multidimensional Berry-Esseen inequality on a closed sphere, a half plane and a rectangular set.

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